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IEEE POWER ELECTRONICS REGULAR PAPER 1
Natural Boundary Transition and Inherent Dynamic
Control of a Hybrid-Mode Modulated
Dual-Active-Bridge Converter
Jingxin Hu, Member, IEEE, Shenghui Cui, Member, IEEE, Rik W. De Doncker, Fellow, IEEE
Abstract—This article proposes a hybrid-mode modulation
strategy for the single-phase dual-active-bridge (DAB) dc-dc con-
verter that realizes soft-switching in the whole operating range.
Different from existing modulation methods that are usually
dependent on complex mathematical optimization processes, the
presented study reveals that the simple trapezoidal continuous
conduction mode and triangular discontinuous conduction mode
inspired by a quasi-single-active-bridge operation can naturally
and sequentially extend the soft-switching boundary of the
conventional single-phase-shift (SPS) modulation to the full range
in both the buck and boost modes. Meanwhile, the transformer
rms current is also reduced. Moreover, a fast-dynamic control
with inherent seamless mode transitions is realized by intro-
ducing the predictive-current SPS modulation. The proposed
hybrid-mode modulation strategy with closed-form solutions can
be easily implemented in a generalized closed-loop controller,
which enables an ultra-wide-voltage-range operation of the DAB
converter with significantly elevated efficiency and fast transient
responses. The effectiveness of the proposed method is validated
by comprehensive experimental results from a small-scale DAB
prototype.
Keywords—Dual-active-bridge, dynamic control, modulation
schemes, single-active-bridge, smooth transition, soft-switching,
wide operating voltage range.
I. INTRODUCTION
THE dual-active-bridge (DAB), first proposed in 1988 for
aerospace applications [1], [2], is one of the most popular
bidirectional isolated dc-dc converter topologies. Due to its
attractive features such as inherent soft-switching capability,
buck and boost operation, and high power density, it is ideal
for dc solid-state transformers in grid applications [3]–[6], re-
newable energy integration [7], [8], energy storage systems [9]
as well as more-electric transportation systems [10]–[13].
The single-phase-shift (SPS) is the original and mean-
while the simplest modulation method for the DAB con-
verter [2]. With adequate inductive reactive currents in the
high-frequency ac-link transformer, all power semiconductor
devices can realize zero-voltage switching (ZVS), which leads
Manuscript received June 1, 2021, revised August 27, 2021 and accepted
October 10, 2021. Date of publication October xx, 2021; date of current
version xx xx, xx. (Corresponding author: Shenghui Cui)
Jingxin Hu and Rik W. De Doncker are with the Institute for Power Gen-
eration and Storage Systems, E.ON ERC and FEN Research Campus, RWTH
Aachen University, Aachen 52074, Germany (e-mail: jhu@eonerc.rwth-
aachen.de; post pgs@eonerc.rwth-aachen.de).
Shenghui Cui is with Department of Electrical and Computer Engi-
neering, Seoul National University, Seoul 08826, South Korea (e-mail:
cuish@snu.ac.kr).
This work is supported by European Union’s Horizon 2020 research
and innovation programme under grant agreement No. 957788, project HY-
PERRIDE, and the Federal Ministry of Education and Research (BMBF,
FKZ03SF0490), Flexible Electrical Networks (FEN) Research Campus.
to high-efficiency operation and clean switching waveforms
with low electromagnetic interference (EMI). However, when
the output-to-input voltage ratio deviates greatly from unity
especially under light-load conditions, the DAB converter
will not only lose soft-switching but also suffer from high
rms current. Thus, despite its advantages under the nominal
operating condition, the SPS modulation is not sufficient to
guarantee high-efficiency operation of the DAB converter in
the full operating range.
To address this issue, several alternative modulation
schemes with adjustable duty ratios of the input and output
ac voltages have been proposed in literature, which are com-
prehensively summarized in [14]. In [15], [16], the extended-
phase-shift (EPS) modulation is proposed, which can realize
soft-switching in the full operating range. However, the EPS
modulation still suffers from a relatively high rms current un-
der light-load conditions. Moreover, due to lack of closed-form
solutions, the EPS modulation usually has to be implemented
in look-up-tables, which has considerable constraints in prac-
tical applications. To improve the applicability of this method,
the fundamental-optimal strategy (FOPS) is proposed in [17],
which can be implemented in a unified controller with simple
calculations. However, the maximum power transfer capability
and the soft-switching range are compromised. In [18], the
dual-phase-shift (DPS) modulation is proposed to eliminate the
reactive power and boost the system efficiency. Unfortunately,
it cannot realize full-range soft-switching. Besides, similar
to the EPS, the DPS modulation also lacks a closed-form
solution to its control variables. The triple-phase-shift (TPS)
modulation presented in [19], [20] inherently provides suffi-
cient degrees of freedom to extend the soft-switching range
and meanwhile reduce the rms current. However, it consists
of many possible switching modes which complicates the
parameter determination. The optimal switching pattern and
control variables of the TPS modulation are normally derived
from complex mathematical optimization process [21]–[25].
This usually results in a hybrid-mode operation, which is
not intuitive due to lack of physical insights in the circuit.
Moreover, modulation-mode transitions under transient oper-
ation conditions can induce a transient dc-bias current in the
high-frequency ac-link transformer. This can highly degrade
the dynamic performance of the converter or even cause the
transformer core saturation. Although the transient dc-bias can
be suppressed by dedicated control methods [26]–[30], this
usually requires sophisticated gating logic and increases the
computational complexity of the hybrid-mode operation.
Distinguished from the aforementioned methods, this article
proposes a hybrid-mode modulation strategy that is inspired
IEEE POWER ELECTRONICS REGULAR PAPER 2
by the quasi-single-active-bridge operation. The analysis first
reveals that the ZVS boundary of the SPS modulation in
the buck mode can be naturally and sequentially extended to
the full operating range by the continuous- and discontinuous
conduction modes of the single-active-bridge (SAB) converter.
The switching patterns of the DAB converter are then designed
to emulate the operation waveforms of the SAB converter
in both buck and boost mode respectively, which can cover
the whole hard-switching region of the SPS modulation with
soft-switching and reduced rms current. The resulting hybrid-
mode modulation not only has a natural boundary transition,
but also benefits from closed-form solutions, which enables
simple model-based control implementation. Moreover, with
the predictive-current SPS modulation, the proposed hybrid-
mode modulation can realize inherent dynamic control and
smooth mode transitions without transient dc-bias current.
Notice that the fast-dynamic control does not require any
additional gating logic under transient operation conditions,
which minimizes the complexity of the control algorithm.
Thus, with the proposed method, the DAB converter can
operate in an ultra-wide voltage range with both a high
efficiency and a fast transient response.
It is worth mentioning that the motivation of this paper is
not to provide another globally optimized modulation method
for the DAB converter, but to reveal a simple and intuitive
hybrid-mode modulation method based on the intrinsic circuit
behaviors. Notice that it is also possible to emulate the opera-
tion of a asymmetrical-dual-active-bridge (ADAB) [31], [32],
also known as semi-dual-active-bridge (SDAB) [33], which
has more control freedoms to optimize the performance than
the SAB converter. However, due to multiple control variables,
the ADAB converter still requires a complex optimization pro-
cedure for modulation schemes and dedicated dynamic control
methods to suppress transient dc-bias currents. Therefore, the
ADAB operation is not considered in this paper.
The rest of the article is structured as follows. First, the
proposed hybrid-mode modulation schemes, are introduced
in Section II with their origin from the SAB operation and
the corresponding closed-form solutions. This is followed
by a description of the inherent dynamic control and the
implementation of the unified voltage control in Section III.
Furthermore, in Section IV, the proposed modulation and
control methods are verified by comprehensive experimental
results from a small-scale laboratory prototype. Finally, Sec-
tion V concludes this article.
II. MODULATION SCHEMES
The single-phase DAB converter consists of two H-bridges
linked by a high-frequency ac transformer, as depicted in
Fig. 1. The total leakage inductance 𝐿𝜎is employed as
the energy transfer element, whose current is driven by the
difference between the ac voltages of the input and output
bridges, i.e. 𝑣AB and 𝑣CD, respectively. The DAB converter
normally has three control variables, which are the duty ratios
𝐷pand 𝐷sof the input and output ac voltages respectively,
and the phase-shift ratio 𝐷𝜑between two bridges.
ip
S1
ABCD
Lσ
S2
S3
S4
Q1
Q2
Q3
Q4
is,dc
isC
iload
Fig. 1: Circuit diagram of single-phase DAB converter.
0Ts/2 Ts
0
DpTs
ip
is,dc
is,dc
0
0Ts/2 Ts
0
DpTs
ip
is,dc
is,dc
0
DsTs
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
(a) (b)
(c)
ZVS Region
Hard-Swithing
Input Bridge
Hard-Swithing
Output Bridge
1
23
DsTs
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
Fig. 2: Key operation waveforms and characteristics of the SPS modulation.
(a) Typical ZVS operation waveforms; (b) Operation waveforms at the ZVS
boundary in the buck mode; (c) ZVS region.
A. Single-Phase-Shift Modulation and Its ZVS Boundary
As the original method, the SPS modulation is still one
of the most commonly used operation schemes for the DAB
converter due to its simplicity. As shown in Fig. 2(a), in the
SPS modulation, 𝐷pand 𝐷sare fixed to 0.5, and only 𝐷𝜑is
employed as the control variable to change the power flow. For
sake of simplicity, only the positive power flow is hereinafter
considered. The transformer current 𝑖pcan be expressed by
piecewise linear functions [2], whereby the averaged output
dc current 𝐼s−dc and its maximum value are calculated as
𝐼s,dc =
𝑁tr𝑉p𝐷𝜑(1−2𝐷𝜑)
𝑓 𝐿 𝜎
,(1)
𝐼s,dc,max =
𝑁tr𝑉p
8𝑓 𝐿 𝜎
,at 𝐷𝜑=0.25.(2)
where 𝑁tr denotes the turns ratio of the transformer, 𝑉pdenotes
the input dc voltage, and 𝑓denotes the switching frequency.
According to (1), in the SPS modulation, 𝐼s,dc is independent
of the output dc voltage 𝑉s. Furthermore, 𝐷𝜑is calculated by
𝐷𝜑=
1
4· 1−1−8𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p!.(3)
IEEE POWER ELECTRONICS REGULAR PAPER 3
ip
S1
ABCD
Lσ
S2
S3
S4
Q1
Q2
Q3
Q4
is,dc
isC
iload
Fig. 3: Circuit diagram of single-phase SAB converter.
When the transformer current flows into the anti-parallel
diodes at the turn-on instant of the corresponding switch, ZVS
turn-on is realized. This leads to the soft-switching condition
𝑖p(0)=(𝑑−1−4𝑑𝐷 𝜑)𝑉p
4𝑓 𝐿 𝜎≤0,for input bridge,
𝑖p(𝐷𝜑𝑇s)=(4𝐷𝜑−1+𝑑)𝑉p
4𝑓 𝐿 𝜎≥0,for output bridge,
(4)
where 𝑑=𝑁tr𝑉s/𝑉pdenotes the dc voltage ratio, and 𝑇s=1
/𝑓
denotes the switching period.
Fig. 2(b) depicts the operation waveforms under the ZVS-
boundary condition of the SPS modulation in buck mode
(𝑑 < 1), where the switches in the output bridge realize zero-
current-switching (ZCS) turn-off. Substituting (4) into (1), the
ZVS boundary of the SPS modulation can be identified in (5),
which is also shown in Fig. 2(c). It can be observed that, in
the SPS modulation, the DAB converter realizes soft-switching
when the voltage ratio is close to unity and the load current
is relatively high. Moreover, the hard-switching regions of the
output bridge and the input bridge are located in the buck
mode (𝑑 < 1) and the boost mode (𝑑 > 1), respectively.
𝐼s,dc ≥𝑁tr𝑉p(𝑑2−1)
8𝑓 𝐿 𝜎𝑑2,for input bridge,
𝐼s,dc ≥𝑁tr𝑉p(1−𝑑2)
8𝑓 𝐿 𝜎
,for output bridge.
(5)
B. Operation Boundary of a Single-Active-Bridge Converter
When the gating signals of the switches in the output bridge
are disabled, the output bridge operates as a diode rectifier. The
circuit topology effectively turns into a single-phase single-
active-bridge (SAB) converter as depicted in Fig. 3. The SAB
is a unidirectional isolated buck-type dc-dc converter, which
regulates the power flow by adjusting the duty ratio 𝐷pof
the input ac voltage [2]. Due to the existence of the output
diode rectifier, the transformer current is always in phase with
the output ac voltage, which leads to the ZCS turn-off of the
diode rectifier. Dependent on the load condition, the SAB con-
verter can operate in either the continuous conduction mode
(CCM) or the discontinuous conduction mode (DCM) [34]–
[36], which are described in detail as follows. Since the output
bridge is not switched in the SAB converter, the variables 𝐷𝜑
and 𝐷sin Section II-B represent the equivalent external and
internal phase-shift ratios judged from the voltage waveforms
of the SAB converter.
1) CCM: The SAB converter operates in the CCM at a
relatively high load current. As depicted in Fig. 4(a), the
input ac voltage 𝑣AB leads the output ac voltage 𝑣CD with an
equivalent phase-shift ratio 𝐷𝜑≥0. The transformer current
0Ts/2 Ts
0
DpTs
t1t2
ip
is,dc
is,dc
0
SAB
DsTs
S1S2
S3S4
S4
Q1, Q4Q2, Q3
DAB
0Ts/2 Ts
t1t2
SAB
S1S2
S3
S4
Q1Q2
DAB
S4
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
DφTs
(a) (b)
Fig. 4: Key operation waveforms of the SAB converter and the quasi-SAB
operation in the buck mode. (a) Trapezoidal continuous conduction mode
(buck); (b) Triangular discontinuous conduction mode (buck).
is continuous with a trapezoidal waveform. Therefore, it is
hereinafter named as trapezoidal CCM (TZ-CCM-Buck). In
the TZ-CCM-Buck mode, the equivalent duty ratio 𝐷sof
the output bridge is always 0.5. The input bridge can realize
ZVS turn-on, while the output bridge can realize ZCS turn-
off. Therefore, hard-switching with a diode reverse recovery
is avoided under this condition.
The transformer current of the TZ-CCM-Buck mode can
also be expressed by piecewise linear functions [2]. The
expression of 𝐷𝜑is given by
𝐷𝜑=
1−𝑑
4,(6)
which is only related to the voltage ratio 𝑑.
The relationship between 𝐼s,dc and 𝐷pis described as:
𝐼s,dc =
𝑁tr𝑉p(−4𝐷2
p+4𝐷p−𝑑2)
8𝑓 𝐿 𝜎
.(7)
Thereby, 𝐷pis calculated as
𝐷p=
1
2−1−𝑑2
4−2𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p
.(8)
For a given voltage ratio 𝑑, the maximum output dc current
is obtained at 𝐷p=0.5, while the minimum output dc
current is obtained at 𝐷p=𝑑
2. Therefore, the upper and lower
boundaries of the TZ-CCM-Buck mode are defined as
𝐼s,dc,max =
𝑁tr𝑉p(1−𝑑2)
8𝑓 𝐿 𝜎
,(9a)
𝐼s,dc,min =
𝑁tr𝑉p𝑑(1−𝑑)
4𝑓 𝐿 𝜎
,(9b)
which are plotted in Fig. 5. Comparing (5) and (9a), one can
easily identify that the upper boundary of the TZ-CCM-Buck
mode is also the ZVS boundary of the SPS modulation in the
buck mode, where the operation waveforms of two modes are
identical as shown in Fig. 2(b).
2) DCM: The SAB converter operates in the DCM at a
lower load current. The transformer current is discontinuous
with a triangular waveform, as depicted in Fig. 4(b). Therefore,
it is hereinafter named as triangular DCM (TR-DCM-Buck).
In the TR-DCM-Buck mode, 𝐷schanges with 𝐷paccording to
IEEE POWER ELECTRONICS REGULAR PAPER 4
ZVS-SPS
1
2a
TZ-CCM
(buck)
2b
TR-DCM
(buck)
3a
TZ-CCM
(boost)
3b
TR-DCM
(boost)
Eq.(9a)
Eq.(9b)
Eq.(15a)
Eq.(15b)
Eq.(2)
Fig. 5: Operation range of the proposed hybrid-mode modulation.
𝐷s=
𝐷p
𝑑.𝐷𝜑is defined as 𝐷𝜑=
𝐷s−𝐷p
2=𝐷s(1−𝑑)
2. As shown
in Fig. 4(b), half of the switches in the input bridge can realize
ZVS turn-on, and the other half can realize ZCS turn-off as
the output bridge. Therefore, no hard-switching operation with
a diode reverse recovery occurs under this condition.
The average output dc current with its maximum and
minimum values is given by
𝐼s,dc =
4𝑁tr𝑉p𝑑𝐷2
𝜑
(1−𝑑)𝑓 𝐿 𝜎
,(10)
𝐼s,dc,max =
𝑁tr𝑉p𝑑(1−𝑑)
4𝑓 𝐿 𝜎
,at 𝐷𝜑=
1−𝑑
4,(11a)
𝐼s,dc,min =0,at 𝐷𝜑=0.(11b)
From (10), 𝐷𝜑is calculated as
𝐷𝜑=(1−𝑑)𝑓 𝐿 𝜎𝐼s,dc
4𝑑𝑁tr𝑉p
.(12)
The operation range of the TR-DCM-Buck mode is depicted
in Fig. 5, which has a natural boundary transition from the
TZ-CCM-Buck mode. Fig. 6 further shows the operation
waveforms under the boundary condition. Therefore, with a
combination of the TZ-CCM-Buck, TR-DCM-Buck and SPS
modulation modes, as depicted in Fig. 5, the DAB converter
can realize full-range soft-switching in the buck mode.
Although the SAB operation can extend the soft-switching
range of the DAB converter, it also has several constraints:
1) In the TR-DCM-Buck mode, the operation state of the
output diode rectifier is undefined in the zero-current interval,
which will result in a high-frequency oscillation of 𝑣CD due to
parasitics in the circuit. This can potentially cause EMI issues.
2) If unipolar transistors, e.g. MOSFETs, are employed, the
SAB operation cannot take the advantage of the synchronous
rectification to reduce the conduction loss in the output bridge.
3) Most importantly, the SAB operation is only valid in the
buck mode.
C. Proposed Hybrid-Mode Modulation with Natural Bound-
ary Transition
To tackle these issues, a hybrid-mode modulation is pro-
posed for the DAB converter to imitate the SAB operation in
the whole hard-switching region of the SPS modulation.
0t2=Ts/2 Ts
t1
SAB
S1S2
S3
S4
Q1Q2
DAB
S4
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
Fig. 6: Operation waveforms of the boundary condition between the TZ-
CCM-Buck and TR-DCM-Buck modes.
(a) (b)
0Ts/2 Ts
0
t1t2
ip
is,dc
is,dc
0DsTs
S1, S4S2, S3
Q3
Q4
DφTs
DpTs
Q1Q2
0Ts/2 Ts
t1t2
S1S2
S3
S4
Q1Q2
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
0
0
Fig. 7: Key operation waveforms in the boost mode. (a) Trapezoidal continu-
ous conduction mode (boost); (b) Triangular discontinuous conduction mode
(boost).
1) TZ-CCM-Buck and TR-DCM-Buck: In the buck mode,
the same TZ-CCM-Buck and TR-DCM-Buck modes are em-
ployed except for applying the synchronous rectification tech-
nique. As shown in Fig. 4, according to the derived closed-
form solutions in Section II-B, the devices in the output
bridge are switched to generate exactly the same ac voltage
waveform as the SAB converter in these two modes. Thus,
the output bridge can not only maintain ZCS turn-off, but
also reduce the conduction loss due to lower on-state voltage
of MOSFETs than the forward voltage of diodes. Moreover,
since a zero-voltage state is defined for 𝑣CD in the zero-current
interval in the TR-DCM-Buck mode, the EMI issue due to
an oscillating ac voltage can be avoided. It should be also
noticed that the TZ-CCM-Buck and TR-DCM-Buck modes
are effectively special conditions of the EPS modulation and
the TPS modulation, respectively.
2) TZ-CCM-Boost and TR-DCM-Boost: To achieve the
similar operation performance in the boost mode, the TZ-
CCM-Buck and TR-DCM-Buck modes are mirrored and
modified to the TZ-CCM-Boost and TR-DCM-Boost modes,
respectively, as depicted in Fig. 7.
As shown in Fig. 7(a), the TZ-CCM-Boost mode maintains
a continuous trapezoidal current waveform. However, as a
mirrored version of the TZ-CCM-Buck mode, 𝐷pis fixed to
0.5, while 𝐷salong with 𝐷𝜑is adapted to realize ZCS turn-
off of the switches in the input bridge. Meanwhile, the output
bridge can realize ZVS turn-on. The transformer current can
IEEE POWER ELECTRONICS REGULAR PAPER 5
be similarly expressed in piecewise linear functions. The ZCS
turn-off condition of 𝑖p(0)=𝑖p(𝑇s
2)=0yields
𝐷𝜑=
𝑑−1
4𝑑(13)
The averaged output dc current with its maximum and
minimum values of the TZ-CCM-Boost mode is given by
𝐼s,dc =
𝑁tr𝑉p(−4𝑑2𝐷2
s+4𝑑2𝐷s−1)
8𝑑2𝑓 𝐿 𝜎
,(14)
𝐼s,dc,max =
𝑁tr𝑉p(𝑑2−1)
8𝑑2𝑓 𝐿 𝜎
,at 𝐷s=
1
2,(15a)
𝐼s,dc,min =
𝑁tr𝑉p(𝑑−1)
4𝑑2𝑓 𝐿 𝜎
,at 𝐷s=
1
2𝑑.(15b)
From (14), 𝐷sin the TZ-CCM-Boost mode is obtained by
𝐷s=
1
2−𝑑2−1
4𝑑2−2𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p
.(16)
According to (15a) and (15b), the operation region of the
TZ-CCM-Boost mode is depicted in Fig. 5, which transits
naturally from the ZVS boundary of the SPS modulation.
The last remaining piece of the hard-switching region in
Fig. 5 is finally covered by the TR-DCM-Boost mode, which
is derived by mirroring the switching pattern of the TR-DCM-
Buck mode as depicted in Fig. 7(b). To realize the desired
discontinuous triangular current waveform, 𝐷p=𝑑𝐷sneeds
to be maintained. Thus, 𝐷𝜑is defined as 𝐷𝜑=(𝑑−1)𝐷s
2. In
this mode, half of the switches in the output bridge can realize
ZVS turn-on, while the remaining switches in both the input
and output bridges can realize ZCS turn-off.
The averaged output dc current with its maximum and
minimum values of the TR-DCM-Boost mode is given by
𝐼s,dc =
4𝑁tr𝑉p𝐷2
𝜑
(𝑑−1)𝑓 𝐿 𝜎
,(17)
𝐼s,dc,max =
𝑁tr𝑉p(𝑑−1)
4𝑓 𝐿 𝜎𝑑2,at 𝐷𝜑=
𝑑−1
4𝑑,(18a)
𝐼s,dc,min =0,at 𝐷𝜑=0.(18b)
From (10), 𝐷𝜑in the TR-DCM-Boost mode is obtained by
𝐷𝜑=(𝑑−1)𝑓 𝐿 𝜎𝐼s,dc
4𝑁tr𝑉p
.(19)
The operation region of the TR-DCM-Boost mode is de-
picted in Fig. 5, which further extends the soft-switching range
towards no-load conditions with a natural boundary transition
from the TZ-CCM-Boost mode.
Therefore, combining the SPS, TZ-CCM-Buck, TR-DCM-
Buck, TZ-CCM-Boost and TR-DCM-Boost modes, the DAB
converter can realize full-range soft-switching with seamless
mode transitions. It is worth mentioning that the natural bound-
ary transition is not only for the output dc current, but also for
control variables in the switching patterns as depicted in Fig. 8.
It is shown that in both the buck and boost modes the control
variables, i.e. 𝐷𝜑,𝐷pand 𝐷s, change continuously between
two adjacent modulation modes. Moreover, according to the
derived expressions of the rms current for these modulation
TR-DCM-Buck TZ-CCM-Buck SPS TR-DCM-Boost TZ-CCM-Boost SPS
(a) (b)
Fig. 8: Control variables 𝐷𝜑,𝐷pand 𝐷sof the proposed modulation method
at a variable output dc current. (a) At 𝑑=0.5. (b) At 𝑑=1.5.
dc
dc
Fig. 9: Ratio between the rms current and the output dc current in the whole
operating range.
TABLE I: Expressions of the transformer rms current in different modulation
modes.
Mode Expression of 𝐼p,rms
SPS √3𝑁tr𝑉p
12 𝑓 𝐿𝜎−64𝑑 𝐷3
𝜑+48𝑑𝐷 2
𝜑+ (𝑑−1)2
TZ-CCM-Buck √3𝑁tr𝑉p
6𝑓 𝐿𝜎−(2𝐷p−𝑑)3
2+ (𝑑−1)2(3(2𝐷p−𝑑)2
4+3(2𝐷p−𝑑)
2+𝑑2)
TR-DCM-Buck 4𝑁tr𝑉p𝑑𝐷 𝜑
𝑓 𝐿𝜎𝐷𝜑
3(1−𝑑)
TZ-CCM-Boost √3𝑁tr𝑉p
6𝑑 𝑓 𝐿𝜎−𝑑(2𝑑 𝐷s−1)3
2+ (𝑑−1)2(3(2𝑑 𝐷s−1)2
4+3(2𝑑𝐷s−1)
2+1)
TR-DCM-Boost 4𝑁tr𝑉p𝐷𝜑
𝑓 𝐿𝜎𝑑 𝐷𝜑
3(𝑑−1)
modes as given in Table. I, the large rms current in the
hard-switching region of the SPS modulation is significantly
reduced by the proposed hybrid-mode modulation method, as
depicted in Fig. 9.
III. INHERENT DYNAMIC CONT ROL
When the DAB converter operates under transient condi-
tions, the switching pattern along with its control variables
𝐷p,𝐷sand 𝐷𝜑can dynamically change, which leads to
either a state change in the same modulation mode or a
mode transition. When the initial steady-state currents of two
consecutive switching patterns are different, a transient dc-
bias is induced in the transformer current. This can result in
degraded transient performance or even cause transformer core
saturation. Therefore, the dynamic current control is necessary
for the hybrid-mode operation of the DAB converter.
The aforementioned CCM and DCM in both the buck and
boost modes have a common feature, which is ZCS turn-off of
the switches. Therefore, it is convenient to align the starting
IEEE POWER ELECTRONICS REGULAR PAPER 6
0Ts/2 Ts
0
ip
is,dc
is,dc
0
(a)
Ts/2 Ts
ip
S1S2
Q1Q2
S4S3
Q4Q3
0
-Ts/2
-Ts
S1S2
S3
S4
Q1Q2
Q4Q3
0
TR-DCM-Buck SPS
(b)
tx
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
Fig. 10: Key operation waveforms of the inherent dynamic control. (a)
Predictive-current SPS modulation; (b) Mode transition from the TR-DCM-
Buck to the predictive-current SPS modulation.
instant of the switching pattern with a ZCS turn-off instant in
each switching cycle. Specifically, the starting instant of the
switching period in both the TZ-CCM-Buck and TR-DCM-
Buck modes is aligned with the rising edge of the positive 𝑣CD
at 𝑖p=0, as depicted in Fig. 4. For the TZ-CCM-Boost and
TR-DCM-Boost modes, the starting instant of the switching
pattern is aligned with the rising edge of the positive 𝑣AB at
𝑖p=0, as depicted in Fig. 7. Thereby, the initial and ending
steady-state currents in these modulation modes are always
zero, which inherently avoids a transient dc-bias current.
A. Predictive-Current Single-Phase-Shift for Smooth Mode
Transitions
Different from the CCM and DCM modes, the SPS mod-
ulation usually does not have a ZCS turn-off instant of
switches except for the ZVS boundary condition. To enable a
smooth mode transition without a transient dc-bias current, the
starting instant of the switching pattern needs to be determined
by predicting the zero-crossing of the transformer current.
Fortunately, as depicted in Fig. 10(a), the zero-crossing of 𝑖pis
always in the phase-shift interval between the rising edges of
𝑣AB and 𝑣CD, since only the ZVS region of the SPS modulation
is considered in the proposed method. Based on the derived
expression of the piecewise linear current [2], the time interval
𝑡xbetween the rising edge of 𝑣AB and the current zero-crossing
can be calculated by
𝑡x=
4𝑑𝐷 𝜑+1−𝑑
4(1+𝑑)𝑓.(20)
By delaying the starting instant of the switching pattern with a
time interval of 𝑡xfrom the rising edge of 𝑣AB, the initial and
DAB
Vs
Vs
*
PI
Vs
Vp
Mode selection &
Calculate control
parameters
Pulse
generator
Dφ
Dp
Ds
Iload
Iout
Fig. 11: Generalized closed-loop control block diagram for the DAB converter.
Update Parameter:
d, VP,and Is,dc ≥0
Boundary calculation:
Is,dc,max,1
for SPS with (2)
Is,dc,max,2
for TZ-CCM-Buck with (9a)
Is,dc,max,3
for TR-DCM-Buck with
Is,dc,max,4
for TZ-CCM-Boost with (15a)
Is,dc,max,5
for TR-DCM-Boost with (18a)
SPS
Dφ= 0.25
Dp= 0.5
Ds= 0.5
SPS
Dφwith (3)
Dp= 0.5
Ds= 0.5
Is,dc <Is,dc,max,1
TZ-CCM-Boost
Dφ
Dp= 0.5
Ds
Is,dc <Is,dc,max,4
TR-DCM-Buck
Dφwith ( )
Dp=dDs
Ds= 2Dφ/(1
-
d)
Is,dc <Is,dc,max,3
TZ-CCM-Buck
Dφwith ( )
Dp
Ds= 0.5
Is,dc <Is,dc,max,2
TR-DCM-Boost
Dφ
Dp=dDs
Ds= 2Dφ/(d-1)
Is,dc <Is,dc,max,5
Yes
No
Yes
No
No
Yes
Yes
Yes
No
No
with ( )
with ( )
(11a)
12 19 6
with ( )
8
13
with ( )
16
Fig. 12: Flowchart of the model-based feed-forward function.
ending steady-state currents of the SPS modulation are also
zero, as depicted in Fig. 10(a). Thus, the DAB converter can
inherently realize a dynamic current control and smooth mode
transitions as shown in Fig. 10(b). Compared to other methods
that suppress the induced transient dc-bias current [26]–[30],
the proposed modulation methods inherently avoids this issue,
which improves the transient performance with minimized
computational efforts.
B. Unified Hybrid-Mode Voltage Control
The proposed hybrid-mode modulation strategy can be
implemented in a generalized closed-loop voltage controller, as
depicted in Fig. 11. The output dc voltage is simply controlled
by a PI regulator, which generates a reference output dc cur-
rent. With the derived closed-form solutions for the modulation
modes in Section II, a model-based feed-forward function is
constructed, which selects the suitable modulation mode and
directly calculates the corresponding control variables based
on the measured dc voltage ratio and reference output dc
current. Such kind of model-based feed-forward control is
beneficial to improve the dynamic performance of the DAB
converter [37]. Fig. 12 presents the flowchart of the model-
based feed-forward function. As depicted in Fig. 11, the feed-
forward path of 𝐼load can be implemented to constitute the
reference output dc current together with the output of the
voltage PI regulator. Thereby, the closed-loop control has a
better capability of rejecting the load disturbance, leading
to a faster load transient response. Notice that the steady-
state switching pattern of each mode is pre-calculated with
zero initial current as illustrated in Section III-A, a dedicated
dynamic controller to calculate the transient switching pattern
is no longer required.
IEEE POWER ELECTRONICS REGULAR PAPER 7
(a) (b)
Output DC Voltage
Inductor current
39.6
39.8
40.0
Time in second
0.18 0.20 0.22 0.24 0.26 0.28
-10
0
10
Output DC Voltage
Inductor current
39.7
39.8
39.9
40.0
× 1e-1
Time in second
1.998 2.000 2.002 2.004
-10
0
10
Current in A Voltage in V
Current in A Voltage in V
No mismatch
Lσ,actual=1.2Lσ
No mismatch
Lσ,actual=1.2Lσ
Fig. 13: Simulation results of a load step response with the proposed
control method considering tolerance in the leakage inductance. Simulation
parameters are 𝑉p=80 V,𝑉s=40 V,𝑁tr =1,𝑓=20 kHz,𝐿𝜎=39 µH,
output capacitance 𝐶out =1 mF, proportional gain 𝐾P=0.83 and integral
gain 𝐾I=34.74. (a) Full-time view. (b) Zoom-in view.
C. Discussion on Parameter Tolerance and Nonlinearities
As the proposed current control is based on feed-forward
functions, the parameter tolerance particularly in the induc-
tance value can influence the operation of the DAB converter.
Take the TR-DCM-Buck mode as an example, the phase-shift
ratio 𝐷𝜑,calc is calculated based on the reference output dc
current 𝐼s,dc,ref and the leakage inductance 𝐿𝜎according to
(12).
𝐷𝜑,calc =(1−𝑑)𝑓 𝐿 𝜎𝐼s,dc,ref
4𝑑𝑁tr𝑉p
(21)
Assuming the actual leakage inductance is 𝐿𝜎 ,actual =𝑘·𝐿𝜎
with a scaling factor 𝑘, it yields to an actual output dc current
by substituting (21) in (10),
𝐼s,dc,actual =
4𝑁tr𝑉p𝑑𝐷2
𝜑,calc
(1−𝑑)𝑓 𝐿 𝜎,actual
=
𝐼s,dc,ref
𝑘,(22)
which is scaled by 1
/𝑘compared to the reference value.
This introduces an error of (1−1
/𝑘)𝐼s,dc,ref in the output
dc current. Due to the existence of the voltage PI regulator
in the controller as shown in Fig. 11, the reference output
dc current 𝐼s,dc,ref will be adapted to compensate the error
caused by the leakage inductance. Therefore, the dynamic
response of the DAB converter will be clearly slower with a
tolerance in the leakage inductance, as shown in the simulation
result in Fig. 13(a). However, since the relationships of control
variables 𝐷𝜑,𝐷pand 𝐷sare independent from the leakage
inductance in the proposed method, the triangular inductor
current with ZCS turn-off can still be realized even with a
tolerance in the leakage inductance, as shown in Fig. 13(b).
Moreover, it is worth mentioning that the accurate parameter
of the leakage inductance in the DAB converter can be
identified online using the method proposed in [38]. Thereby,
the model parameter can be continuously updated to improve
the dynamic response of the DAB converter.
It should be also mentioned that the nonlinearties such as
dead time and parasitic capacitance have some impacts on
the instant current calculations, which can be addressed with
dedicated methods. In [39], the dead time can be effectively
compensated in the triangular and trapezoidal modulation to
mitigate the distortion effect. The parasitic capacitance can
be compensated by the charge-based modulation as proposed
in [40], which, however, inevitably increases the computational
XRS 7070 Real-Time
Simulator/Controller
DAB #1
Device under Test DAB #2
DC Source
Adapter boards
Fig. 14: Experiment setup.
Parameter Value
Input dc voltage 80 V
Total leakage inductance 39 µH
Transformer turns ratio 1:1
Switching frequency 20 kHz
Output capacitance 1 mF
Dead time 1.0µs
TABLE II: Experimental parameters.
efforts. Another possible approach is to compensate the non-
linear effects in the trapezoidal and triangular modulation by
empirically correcting the switching timings according to [41],
which requires parameter tuning through experiments.
IV. EXP ER IM EN TAL VERIFICATIO N
A small-scale DAB converter prototype, as shown in Fig. 14,
is built to verify the proposed modulation and control methods.
Detailed parameters of the prototype are given in Table II.
A second DAB converter with the same specifications is
employed to circulate the power in the experiments. The input
voltage is always fixed to 80 V. An XRS 7070 real-time
controller from AixControl is employed for the experimental
implementation, which is internally based on a DSP+FPGA
architecture. Considering the simple switching patterns and
the fair computational complexity, the proposed control can
also be easily implemented on other control platforms such as
commercial DSPs or FPGAs with DSP slices.
A. Comparison with the SAB Operation
Fig. 15(a) shows the calculated operation boundary of the
hybrid-mode modulation for the converter prototype. At a
fixed voltage ratio 𝑑=0.5, the output dc current is gradually
increased to identify the boundaries of operation modes in both
the SAB operation and the proposed hybrid-mode modulation.
Fig. 15(b)-(e) show the operation waveforms of four operation
points P1-P4, which correspond to the TR-DCM-Buck mode
with 𝐼s,dc =4 A, the boundary condition between the TR-
DCM-Buck and the TZ-CCM-Buck modes with 𝐼s,dc =6.7 A,
the TZ-CCM-Buck mode with 𝐼s,dc =8 A, and the boundary
condition between the TZ-CCM-Buck and the SPS modes with
𝐼s,dc =9.5 A, respectively. It is shown that the waveforms
of the DAB converter match very well with the SAB con-
verter in different operation modes, where the triangular and
trapezoidal transformer current with ZCS turn-off of switches
are realized. Besides, the natural boundary transitions between
the modulation modes are also verified, which coincide with
the theoretical analysis. Moreover, it can also be found in
Fig. 15(b) that the high-frequency oscillation of 𝑣CD in the
TR-DCM-Buck mode of the SAB converter is successfully
eliminated by the DAB operation. As shown in Fig. 15(f),
compared to the SAB operation, the efficiency of the DAB
converter with the proposed modulation increases by 2−2.7 %
over the whole load range at 𝑑=0.5due to the synchronous
rectification.
B. Steady-State Performance
Furthermore, the steady-state performance of the proposed
method is compared with the conventional SPS modulation,
IEEE POWER ELECTRONICS REGULAR PAPER 8
μ
(a) (b)
(c) (d)
(e) (f)
P1
P2
P3
P4
μμ
μ
Fig. 15: Comparison of the SAB operation and the proposed hybrid-mode
modulation. (a) Operation boundary of the DAB prototype; (b) Experimental
waveforms of the TR-DCM-Buck mode at point P1; (c) Experimental wave-
forms of the boundary condition between TR-DCM-Buck and TZ-CCM-Buck
at point P2; (d) Experimental waveforms of the TZ-CCM-Buck mode at point
P3; (e) Experimental waveforms of the boundary condition between TR-CCM-
Buck and SPS at point P4; (f) Measured efficiency curves at 𝑑=0.5.
the FOPS modulation [17] and the optimal TPS modula-
tion [24] under different operation conditions. Fig. 16 shows
the operation waveforms at 𝑉s=60 V and 𝐼s,dc =1 A, which
correspond to the hard-switching operation in the SPS mod-
ulation as well as the TR-DCM-Buck mode in the proposed
method. Although soft-switching can also be realized by the
FOPS modulation as depicted in Fig.16(b), the transformer
rms current is obviously larger than the TR-DCM-Buck mode.
Moreover, the proposed modulation yields the same switching
pattern as the optimal TPS modulation as shown in Fig. 16(c)
and (d). Fig. 17 shows the operation waveforms at 𝑉s=40 V
and 𝐼s,dc =8 A, which corresponds to the TZ-CCM-Buck
mode in the proposed method. This operating point is beyond
the operation range of the FOPS modulation. It is shown that
the optimal TPS modulation and the proposed TZ-CCM-Buck
mode can realize ZVS and ZVS/ZCS operation, respectively,
with comparable rms currents. Fig. 18 and Fig. 19 further show
the operation waveforms in the boost mode at 𝑉s=100 V with
𝐼s,dc =2 A and 𝐼s,dc =4.7 A, respectively. In these two cases,
both the SPS modulation and FOPS modulation suffer from
hard-switching. Meanwhile, the DAB converter operates in the
TR-DCM-Boost and TZ-CCM-Boost modes in the proposed
method, respectively, which realize ZVS/ZCS operation via
the triangular or trapezoidal current. From both the optimal
TPS modulation and the proposed method, it can be found
that the triangular inductor current results in the lowest rms
value in the low-power range. Although ZCS turn-off can
avoid the diode reverse recovery, there is still turn-on loss due
C7 C7
(a) (b)
(c)
vAB: 20V/div
(d)
C7
vAB: 20V/div vCD: 20V/div
ip: 5A/div
10μs/div Ip,rms=1.71A
C7
vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
10μs/div 10μs/div
10μs/div
Ip,rms=4.24A Ip,rms=2.63A
Ip,rms=1.71A
Fig. 16: Measured waveforms at 𝑉s=60 V and 𝐼s,dc =1 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(d) Proposed method (TR-DCM-Buck).
(c)
(a) (b)
C7
10μs/div
C7
vAB: 20V/div
vCD: 20V/div ip: 5A/div
10μs/div
C7
10μs/div
vAB: 20V/div
vCD: 20V/div ip: 5A/div
vAB: 20V/div
vCD: 20V/div ip: 5A/div
Ip,rms=9.68A Ip,rms=9.02A
Ip,rms=9.07A
Fig. 17: Measured waveforms at 𝑉s=40 V and 𝐼s,dc =8 A. (a) SPS
modulation; (b) Optimal TPS modulation [24]; (c) Proposed method (TZ-
CCM-Buck).
(a) (b)
(c) (d)
C7
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
Ip,rms=3.50A
C7 C7
C7
10μs/div 10μs/div
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
Ip,rms=4.32A Ip,rms=3.83A
Ip,rms=3.50A
Fig. 18: Measured waveforms at 𝑉s=100 V and 𝐼s,dc =2 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(c) Proposed method (TR-DCM-Boost).
to the charge of the device output capacitance. In practice,
the magnetizing current of the transformer can contribute an
additional inductive current to assist the charging/discharging
process of the output capacitance.
The converter efficiency is also measured and compared
among the four modulation methods over a wide operating
range. As shown in Fig. 20(a), at 𝑑=0.5, the optimal TPS
IEEE POWER ELECTRONICS REGULAR PAPER 9
Ip,rms=7.02A Ip,rms=6.86A
Ip,rms=6.81A
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
(a) (b)
(d)
(c)
10μs/div 10μs/div
C7
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
10μs/div Ip,rms=6.79A
Fig. 19: Measured waveforms at 𝑉s=100 V and 𝐼s,dc =4.7 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(d) Proposed method (TZ-CCM-Boost).
Efficiency in %
Efficiency in %
Efficiency in %
(a) (b)
(c)
Fig. 20: Measured efficiency curves of the SPS, the FOPS [17], the optimal
TPS [24] and the proposed modulation method. (a) 𝑉s=40 V, i.e. 𝑑=0.5;
(b) 𝑉s=60 V, i.e. 𝑑=0.75; (c) 𝑉s=100 V, i.e. 𝑑=1.25.
modulation shows the highest efficiency over the whole load
range from 1 A to 10 A, with the peak value of 94.2 % at
𝐼s,dc =2 A. Compared to the optimal TPS modulation, the
proposed method shows a very close performance with the
same peak efficiency and a slightly lower efficiency with a
difference less than 0.2 % in the medium to high load range.
Compared to the SPS modulation, the efficiency improvement
of the proposed method is up to 30.3 %. Besides, the proposed
method also achieves a higher efficiency than the FOPS
modulation due to the reduced rms current. Similar results
are also observed from Fig. 20(b) with 𝑑=0.75, which
verify the significant efficiency improvements of the proposed
method under light-load conditions. It is also found that,
with an increasing load current, the efficiency of the SPS
modulation becomes even higher than the FOPS modulation
due to the reduced rms current. Fig. 20(c) further shows the
efficiency curve at 𝑑=1.25. In this case, the proposed method
and the optimal TPS modulation share the highest light-load
efficiency, which is up to 8.6 % and 5.7 % higher than the
SPS modulation and the FOPS modulation, respectively. When
the SPS modulation is selected in the proposed method at
TR-DCM-Buck
TZ-CCM-Buck
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
: ZVS-on : ZCS-off
Fig. 21: Measured transient waveforms with the operation-mode change from
the TR-DCM-Buck mode with 𝐼s,dc =3 A to the TZ-CCM-Buck mode with
𝐼s,dc =9 A at 𝑉s=40 V.
40μs/div
TR-DCM-Buck
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
40μs/div
TR-DCM-Buck
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
(a)
(b)
transient overshoot
: ZVS-on : ZCS-off
Fig. 22: Measured transient waveforms with the operation-mode change from
the TR-DCM-Buck mode with 𝐼s,dc =3 A to the SPS mode with 𝐼s,dc =7 A at
𝑉s=60 V. (a) Conventional SPS modulation; (b) Proposed predictive-current
SPS modulation.
𝐼s,dc ≥5 A, the FOPS modulation shows a slightly improved
efficiency with less than 0.5 %.
In conclusion, the steady-state performance of the proposed
modulation is very close to the optimal TPS modulation [24],
which is significantly improved compared to the conventional
SPS and the FOPS modulation [17]. However, it should be
noticed that the optimal TPS modulation requires a complex
optimization algorithm to derive the optimal control parame-
ters, while the proposed method is intuitively derived from the
simple SAB operation without any optimization procedure.
C. Load-Transient Performance
The performance of the inherent dynamic control with
the proposed hybrid-mode modulation is validated in load-
IEEE POWER ELECTRONICS REGULAR PAPER 10
(b)
40μs/div
TR-DCM-Boost
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
(a)
40μs/div
TR-DCM-Boost
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
: ZVS-on : ZCS-off
transient overshoot
Fig. 23: Measured transient waveforms with the operation-mode change from
the TR-DCM-Boost mode with 𝐼s,dc =3 A to the SPS mode with 𝐼s,dc =8 A
at 𝑉s=100 V. (a) Conventional SPS modulation; (b) Proposed predictive-
current SPS modulation.
is,dc: 5A/div
vAB: 50V/div vCD: 50V/div ip: 10A/div
transient overshoot
Fig. 24: Measured transient waveforms of the optimal TPS modulation [24]
from 𝐼s,dc =3 A to 𝐼s,dc =9 A at 𝑉s=40V.
transient tests. In Fig. 21, a step change of the load current
from 3 A to 9 A occurs at 𝑉s=40 V, which results in a
smooth transition from the TR-DCM-Buck to the TZ-CCM-
Buck mode without a noticeable transient dc-bias current.
Meanwhile, ZVS turn-on and ZCS turn-off operation can also
be verified in the transient waveforms. Furthermore, Fig. 22
shows a step change of the load current from 3 A to 7 A occurs
at 𝑉s=60 V, where the operation mode changes from the TR-
DCM-Buck to the SPS mode. Compared to the situation with
the conventional SPS modulation as shown in Fig. 22(a), the
proposed predictive-current SPS modulation enables a smooth
mode transition without a transient dc-bias current as shown
in Fig. 22(b). Similar results are observed in Fig. 23, when
the load current changes from 3 A to 8 A at 𝑉s=100 V. The
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 50V/div
200ms/div
SPS SPS
TR-DCM-Buck
TZ-CCM-Buck
Vs=100V
Vs=10V
20μs/div
TR-DCM-Buck
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
20μs/div
TZ-CCM-Buck
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
20μs/div
SPS
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div vCD: 50V/div
ip: 10A/div
(a)
(b)
(c)
(d)
Fig. 25: Measured transient waveforms with ramp changes of the reference
output dc voltage from 100 V to 10 V at a constant load current of 𝐼s,dc =
5.5 A. (a) Whole-process waveforms; (b) Zoomed-in waveforms of the TR-
DCM-Buck mode; (c) Zoomed-in waveforms of the TZ-CCM-Buck mode;
(d) Zoomed-in waveforms of the predictive-current SPS mode.
operation mode changes from the TR-DCM-Boost to the SPS
mode. It is shown that the predictive-current SPS modulation
is also effective to avoid a transient dc-bias current in the boost
IEEE POWER ELECTRONICS REGULAR PAPER 11
mode. Therefore, it is verified that the proposed hybrid-mode
modulation realizes inherent dynamic control with smooth
mode transitions under load-transient conditions.
In contrast, a large transient overshoot current is induced
under the load transient condition with the optimal TPS
modulation [24], as shown in Fig. 24, which takes a few
switching cycles to decay.
D. Wide-Range Voltage Control
The proposed hybrid-mode modulation enables an ultra-
wide-voltage-range operation, which is crucial in many ap-
plications such as black start-up and low-voltage ride through.
Fig. 25 shows the transient waveforms of the DAB converter
operating in the voltage control mode with the proposed
hybrid-mode modulation. As shown in Fig. 25(a), the reference
output dc voltage first ramps down from 100 V to 10 V with
a slope of −0.3 V/ms, and then remains constant at 10 V for
another 300 ms. Thereafter, the reference output dc voltage
ramps up back to 100 V with a slope of 0.3 V/ms. During the
whole transient process, the load current remains constant at
𝐼s,dc =5.5 A. It is shown that the output dc voltage is regulated
to successfully follow the reference even under the low-
voltage-ratio condition, i.e. 𝑑=0.125. With the continuously
changing operating condition, the operation mode changes
smoothly in the sequence of SPS, TZ-CCM-Buck, TR-DCM-
Buck, TZ-CCM-Buck and SPS. Meanwhile, the transformer
current is well regulated without an obvious transient over-
shoot. Moreover, it also verifies that the DAB converter can
deliver the same output dc current under the ultra-low-voltage
condition without increasing the current stress of devices.
Fig. 25(b)-(d) further show the zoomed-in waveforms of the
TR-DCM-Buck, TZ-CCM-Buck and SPS modes, respectively,
which validate the effectiveness of the proposed modulation
in the voltage control mode.
E. Comparison of Modulation Methods
Based on the previous analysis and experimental validations,
the benefits and constraints of the proposed hybrid modulation
can be summarized in Table III compared to several state-of-
the-art modulation methods. Compared to the SPS, FOPS [17]
and conventional trapezoidal and triangular modulation [41],
the proposed hybrid modulation and the optimal TPS modu-
lation [24] have more control variables to realize ZVS/ZCS
soft-switching in the full operating range. Although the op-
timal TPS modulation [24] results in a globally optimized
RMS current, the optimization procedure of control param-
eters requires complex calculations. In contrast, the proposed
modulation is derived intuitively from the SAB operation
which has simple closed-form solutions and does not require
any complex optimization process. Moreover, compared to
the other modulation methods including the optimal TPS,
the proposed modulation can inherently realize smooth mode
transitions without transient overshoot currents. This leads
to a simple implementation of the closed-loop control with
suppressed transients.
TABLE III: Qualitative comparison of different modulation methods.
Mode Number of
variables
Soft-sw.
range
Type of
soft-sw. RMS current Optimization
complexity
Suppressed
transients
SPS [1] 1 Partial ZVS Non-optimal None No
FOPS [17] 2 Partial
(improved) ZVS Sub-optimal Medium No
Trapezoidal and
Triangular
modulation [41]
3Partial
(improved) ZVS/ZCS Sub-optimal Low Yes
Optimal TPS [24] 3 Full ZVS/ZCS Optimal High No
Proposed method 3 Full ZVS/ZCS Sub-optimal None Yes
V. CONCLUSION
In this article, a hybrid-mode modulation strategy with
natural boundary transitions and inherent dynamic control
is proposed for the single-phase DAB converter. Inspired
by the quasi-single-active-bridge operation, four dedicated
modulation modes with the trapezoidal- and triangular current
waveforms are intuitively derived, which can naturally and
sequentially extend the soft-switching boundary of the SPS
modulation to the full operating range with a reduced rms
current. Moreover, with the predictive-current SPS modulation,
zero initial steady-state transformer current is realized in each
of the modulation modes. This enables inherent dynamic
control and smooth mode transitions without any dedicated
transient-current control strategy. The proposed hybrid-mode
modulation with closed-form solutions is implemented in a
unified voltage controller, which allows the DAB converter to
operate in an ultra-wide voltage range with improved overall
efficiency and a fast transient response. The effectiveness
of the proposed modulation and control methods has been
validated by comprehensive experiments on a small-scale DAB
converter prototype.
REFERENCES
[1] R. De Doncker, D. Divan, and M. Kheraluwala, “A three-phase soft-
switched high power density dc/dc converter for high power applica-
tions,” in Conference Record of the 1988 IEEE Industry Applications
Society Annual Meeting, 1988, pp. 796–805 vol.1.
[2] R. W. A. A. De Doncker, D. M. Divan, and M. H. Kheraluwala, “A three-
phase soft-switched high-power-density dc/dc converter for high-power
applications,” IEEE Transactions on Industry Applications, vol. 27,
no. 1, pp. 63–73, Jan 1991.
[3] X. She, A. Q. Huang, and R. Burgos, “Review of solid-state transformer
technologies and their application in power distribution systems,” IEEE
Journal of Emerging and Selected Topics in Power Electronics, vol. 1,
no. 3, pp. 186–198, 2013.
[4] J. E. Huber and J. W. Kolar, “Solid-state transformers: On the origins
and evolution of key concepts,” IEEE Industrial Electronics Magazine,
vol. 10, no. 3, pp. 19–28, 2016.
[5] B. Zhao, Q. Song, J. Li, Q. Sun, and W. Liu, “Full-process operation,
control, and experiments of modular high-frequency-link dc transformer
based on dual active bridge for flexible mvdc distribution: A practical
tutorial,” IEEE Transactions on Power Electronics, vol. 32, no. 9, pp.
6751–6766, Sep. 2017.
[6] J. Hu, “Modulation and dynamic control of intelligent dual-active-bridge
converter based substations for flexible dc grids,” Ph.D. dissertation,
Institute for Power Generation and Storage Systems, E.ON Energy
Research Center, RWTH Aachen University, 2019.
[7] J. Hu, P. Joebges, G. C. Pasupuleti, N. R. Averous, and R. W. De Don-
cker, “A maximum-output-power-point-tracking-controlled dual-active
bridge converter for photovoltaic energy integration into mvdc grids,”
IEEE Transactions on Energy Conversion, vol. 34, no. 1, pp. 170–180,
2019.
IEEE POWER ELECTRONICS REGULAR PAPER 12
[8] T. Liu, X. Yang, W. Chen, Y. Li, Y. Xuan, L. Huang, and X. Hao,
“Design and implementation of high efficiency control scheme of
dual active bridge based 10 kv/1 mw solid state transformer for pv
application,” IEEE Transactions on Power Electronics, vol. 34, no. 5,
pp. 4223–4238, 2019.
[9] S. Inoue and H. Akagi, “A bidirectional dc-dc converter for an energy
storage system with galvanic isolation,” IEEE Transactions on Power
Electronics, vol. 22, no. 6, pp. 2299–2306, Nov 2007.
[10] R. Xie and H. Li, “Fault performance comparison study of a dual
active bridge (DAB) converter and an isolated modular multilevel
DC/DC (im2dc) converter for power conversion module application in
a breaker-less shipboard mvdc system,” IEEE Transactions on Industry
Applications, p. 1, 2018.
[11] G. Buticchi, D. Barater, L. F. Costa, and M. Liserre, “A pv-inspired low-
common-mode dual-active-bridge converter for aerospace applications,”
IEEE Transactions on Power Electronics, vol. 33, no. 12, pp. 10467–
10 477, 2018.
[12] N. H. Baars, J. Everts, H. Huisman, J. L. Duarte, and E. A. Lomonova,
“A 80-kw isolated dc–dc converter for railway applications,” IEEE
Transactions on Power Electronics, vol. 30, no. 12, pp. 6639–6647, Dec
2015.
[13] F. An, W. Song, K. Yang, S. Yang, and L. Ma, “A simple power
estimation with triple phase-shift control for the output parallel dab
dc–dc converters in power electronic traction transformer for railway
locomotive application,” IEEE Transactions on Transportation Electri-
fication, vol. 5, no. 1, pp. 299–310, 2019.
[14] N. Hou and Y. W. Li, “Overview and comparison of modulation
and control strategies for a nonresonant single-phase dual-active-bridge
dc–dc converter,” IEEE Transactions on Power Electronics, vol. 35,
no. 3, pp. 3148–3172, 2020.
[15] G. G. Oggier, R. Leidhold, G. O. Garcia, A. R. Oliva, J. C. Balda,
and F. Barlow, “Extending the zvs operating range of dual active bridge
high-power dc-dc converters,” in 2006 37th IEEE Power Electronics
Specialists Conference, June 2006, pp. 1–7.
[16] G. Oggier, G. O. Garc´
ıa, and A. R. Oliva, “Modulation strategy to
operate the dual active bridge dc-dc converter under soft switching in
the whole operating range,” IEEE Transactions on Power Electronics,
vol. 26, no. 4, pp. 1228–1236, April 2011.
[17] B. Zhao, Q. Song, W. Liu, G. Liu, and Y. Zhao, “Universal high-
frequency-link characterization and practical fundamental-optimal strat-
egy for dual-active-bridge dc-dc converter under pwm plus phase-shift
control,” IEEE Transactions on Power Electronics, vol. 30, no. 12, pp.
6488–6494, 2015.
[18] H. Bai and C. Mi, “Eliminate reactive power and increase system
efficiency of isolated bidirectional dual-active-bridge dc–dc converters
using novel dual-phase-shift control,” IEEE Transactions on Power
Electronics, vol. 23, no. 6, pp. 2905–2914, Nov 2008.
[19] N. Schibli, “Symmetrical multilevel converters with two quadrant dc-
dc feeding,” Ph.D. dissertation, Swiss Federal Institute of Technology
Lausanne (EPFL), 2000.
[20] F. Krismer and J. W. Kolar, “Accurate small-signal model for the
digital control of an automotive bidirectional dual active bridge,” IEEE
Transactions on Power Electronics, vol. 24, no. 12, pp. 2756–2768, Dec
2009.
[21] J. Huang, Y. Wang, Z. Li, and W. Lei, “Unified triple-phase-shift
control to minimize current stress and achieve full soft-switching of
isolated bidirectional dc–dc converter,” IEEE Transactions on Industrial
Electronics, vol. 63, no. 7, pp. 4169–4179, 2016.
[22] F. Krismer and J. W. Kolar, “Closed form solution for minimum
conduction loss modulation of dab converters,” IEEE Transactions on
Power Electronics, vol. 27, no. 1, pp. 174–188, Jan 2012.
[23] N. Hou, W. Song, and M. Wu, “Minimum-current-stress scheme of dual
active bridge dc–dc converter with unified phase-shift control,” IEEE
Transactions on Power Electronics, vol. 31, no. 12, pp. 8552–8561,
2016.
[24] A. Tong, L. Hang, G. Li, X. Jiang, and S. Gao, “Modeling and analysis
of a dual-active-bridge-isolated bidirectional dc/dc converter to minimize
rms current with whole operating range,” IEEE Transactions on Power
Electronics, vol. 33, no. 6, pp. 5302–5316, 2018.
[25] S. Shao, M. Jiang, W. Ye, Y. Li, J. Zhang, and K. Sheng, “Optimal phase-
shift control to minimize reactive power for a dual active bridge dc–dc
converter,” IEEE Transactions on Power Electronics, vol. 34, no. 10, pp.
10 193–10 205, 2019.
[26] J. Hu, S. Cui, D. v. d. Hoff, and R. W. De Doncker, “Generic dynamic
phase-shift control for bidirectional dual-active bridge converters,” IEEE
Transactions on Power Electronics, vol. 36, no. 6, pp. 6197–6202, 2021.
[27] Q. Bu, H. Wen, J. Wen, Y. Hu, and Y. Du, “Transient dc bias elimination
of dual-active-bridge dc–dc converter with improved triple-phase-shift
control,” IEEE Transactions on Industrial Electronics, vol. 67, no. 10,
pp. 8587–8598, 2020.
[28] J. Hu, S. Cui, S. Wang, and R. W. De Doncker, “Instantaneous flux and
current control for a three-phase dual-active bridge dc–dc converter,”
IEEE Transactions on Power Electronics, vol. 35, no. 2, pp. 2184–2195,
2020.
[29] S. Wang, C. Li, K. Wang, Z. Zheng, and Y. Li, “Loss imbalance and
transient dc-bias mitigation in dual active bridge dc/dc converters,” IEEE
Journal of Emerging and Selected Topics in Power Electronics, pp. 1–1,
2020.
[30] B. Zhang, S. Shao, L. Chen, X. Wu, and J. Zhang, “Steady state and
transient dc magnetic flux bias suppression methods for a dual active
bridge converter,” IEEE Journal of Emerging and Selected Topics in
Power Electronics, pp. 1–1, 2019.
[31] W. Li, S. Zong, F. Liu, H. Yang, X. He, and B. Wu, “Secondary-
side phase-shift-controlled zvs dc/dc converter with wide voltage gain
for high input voltage applications,” IEEE Transactions on Power
Electronics, vol. 28, no. 11, pp. 5128–5139, 2013.
[32] H. Wu, Y. Lu, T. Mu, and Y. Xing, “A family of soft-switching dc–dc
converters based on a phase-shift-controlled active boost rectifier,” IEEE
Transactions on Power Electronics, vol. 30, no. 2, pp. 657–667, 2015.
[33] D. Sha, J. Zhang, and Y. Xu, “Improved boundary operation for voltage-
fed semi-dab with zvs achievement and nonactive power reduction,”
IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6179–
6189, 2017.
[34] R. U. Lenke, J. Hu, and R. W. De Doncker, “Unified steady-state
description of phase-shift-controlled zvs-operated series-resonant and
non-resonant single-active-bridge converters,” in 2009 IEEE Energy
Conversion Congress and Exposition, 2009, pp. 796–803.
[35] K. Park and Z. Chen, “Analysis and design of a parallel-connected single
active bridge dc-dc converter for high-power wind farm applications,” in
2013 15th European Conference on Power Electronics and Applications
(EPE), 2013, pp. 1–10.
[36] Y. Sang, A. Junyent-Ferr´
e, and T. C. Green, “Operational principles
of three-phase single active bridge dc/dc converters under duty cycle
control,” IEEE Transactions on Power Electronics, vol. 35, no. 8, pp.
8737–8750, 2020.
[37] N. Hou, W. Song, Y. Li, Y. Zhu, and Y. Zhu, “A comprehensive
optimization control of dual-active-bridge dc–dc converters based on
unified-phase-shift and power-balancing scheme,” IEEE Transactions on
Power Electronics, vol. 34, no. 1, pp. 826–839, 2019.
[38] Z. Guo, Y. Luo, and K. Sun, “Parameter identification of the series
inductance in dab converters,” IEEE Transactions on Power Electronics,
vol. 36, no. 7, pp. 7395–7399, 2021.
[39] J. Hu, Z. Yang, S. Cui, and R. W. De Doncker, “Closed-form asymmet-
rical duty-cycle control to extend the soft-switching range of three-phase
dual-active-bridge converters,” IEEE Transactions on Power Electronics,
vol. 36, no. 8, pp. 9609–9622, 2021.
[40] J. Everts, F. Krismer, J. Van den Keybus, J. Driesen, and J. W. Kolar,
“Optimal zvs modulation of single-phase single-stage bidirectional dab
ac–dc converters,” IEEE Transactions on Power Electronics, vol. 29,
no. 8, pp. 3954–3970, 2014.
[41] D. Goldmann, S. Schramm, and H.-G. Herzog, “Triangular and trape-
zoidal modulation for dual active bridge dc-dc converters with fast
switching semiconductors,” in 2019 21st European Conference on Power
Electronics and Applications (EPE ’19 ECCE Europe), 2019, pp. P.1–
P.10.
IEEE POWER ELECTRONICS REGULAR PAPER 13
Jingxin Hu (Member, IEEE) received the B.S. de-
gree from Northeastern University, Shenyang, China,
in 2010, and the M.Sc. and Dr.-Ing. degrees, with the
highest distinction (summa cum laude), from RWTH
Aachen University, Aachen, Germany, in 2013 and
2019 respectively, all in electrical engineering.
From April to October 2012, he was a research
intern with the ABB Corporate Research Center,
Baden-D¨
attwil, Switzerland. In 2013, he joined the
General Electric Global Research Center, Munich,
Germany. Since October 2014, he has been with
the Institute for Power Generation and Storage Systems, E.ON Energy
Research Center, RWTH Aachen University, where he is currently a Senior
Scientist. Since February 2021, he is also the Research Project Leader at
FEN GmbH, Germany. His research interests include power electronics, solid-
state transformers, MVDC and LVDC distribution systems and applications
of wide-bandgap devices.
Dr. Hu was the recipient of the RWTH Aachen - University of Alberta
Senior Research Fellowship in 2021, the STAWAG Best Dissertation Prize
of RWTH Aachen University in 2019, the Chinese Government Award for
Outstanding Self-Financed Students Abroad in 2019, and the Second Prize
Paper Award of IEEE IPEC (ECCE Asia) in 2018.
Shenghui Cui (Member, IEEE) received the B.S.
degree from Tsinghua University, Beijing, China, in
2012, the M.S. degree from Seoul National Uni-
versity, Seoul, South Korea, in 2014, and the Dr.-
Ing. degree with the highest distinction (summa
cum laude) from RWTH Aachen University, Aachen,
Germany, in 2019, all in electrical engineering.
Since September 2021, Dr. Cui is with Depart-
ment of Electrical and Computer Engineering, Seoul
National University, Seoul, South Korea as an Assis-
tant Professor. From March 2015 to May 2021, he
has been with the Institute for Power Generation and Storage Systems, E.ON
Energy Research Center, RWTH Aachen University, Aachen, Germany, where
he worked as Research Associate and later on Senior Scientist. His research
interests include interaction of power systems and power converters, power
converters in ac/dc utility applications, and applications of wide-band gap
power devices.
Dr. Cui was the recipient of the STAWAG Best Dissertation Prize from
Faculty of Electrical Engineering and Information Technology, RWTH Aachen
University in 2019, the Second Place Prize Paper Award of the IEEE
Transactions on Power Electronics in 2018, the Second Prize Paper Award of
IEEE IPEC (ECCE Asia) in 2018, and the Outstanding Presentation Award
of the IEEE Applied Power Electronics Conference in 2014.
Rik W. De Doncker (Fellow, IEEE) received
the Ph.D. degree in electrical engineering from
Katholieke Universiteit Leuven, Leuven, Belgium,
in 1986.
In 1987, he was a Visiting Associate Professor
with the University of Wisconsin-Madison, Madison,
WI, USA, in 1988, a Senior Scientist with GE
CR&D, Schenectady, NY, USA, and in 1994, Vice
President Technology of SPCO, developing world’s
first MVSTS. Since October 1996, he has been a
Professor with RWTH Aachen University, Aachen,
Germany, leading the Institute for Power Electronics and Electrical Drives.
In 2006, he became the Director of E.ON ERC, RWTH and founded the
Institute for Power Generation and Storage Systems. He leads the RWTH
CAMPUS Cluster Sustainable Energy and the BMBF Flexible Electrical
Networks Research CAMPUS. Since 2010, he has been a Member of the
German National Platform for Electric Mobility, since 2017, of the French
VEDECOM, and since 2016, of the German Academy of Science and
Technology.
He was the recipient of the IEEE IAS Outstanding Achievements Award,
the PES Nari Hingorani Custom Power Award in 2008, the 2013 Newell
Power Electronics Field Award, the 2014 IEEE PELS H. Owen Outstanding
Service Award, RWTH Fellow status in 2015, and the IEEE Gold Medal in
Power Engineering in 2020.
